Higher November 2020 Paper 1 Q14
14
(a) \(c = 2^{10} \times 3 \times 5^6\)
Work out \(18c\).
Give your answer as a product of prime factors in index form. [2 marks]
(b) Work out \(\quad \sqrt[3]{\dfrac{2^7 \times 11^3}{2}}\)
Give your answer as an integer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((18 =)\ 2 \times 3^2\) or \((18 =)\ 2 \times 3 \times 3\) | M1 | oe eg \((18 =)\ 2^1 \times 3^1 \times 3^1\) allow 2, 3 and 3 in a factor tree |
| \(2^{11} \times 3^3 \times 5^6\) | A1 | any order SC1 864 000 000 |
Additional guidance
| M1 may be implied eg1 \(2 \times 3^2 \times 2^{10} \times 3 \times 5^6\) eg2 \(2^{11} \times 3 \times 3 \times 3 \times 5^6\) | M1 M1 |
| Condone a multiplier of 1 for M1 only if not recovered eg1 \(1 \times 2 \times 3 \times 3\) eg2 \(1 \times 2^{11} \times 3^3 \times 5^6\) | M1 M1A0 |
| Allow the prime factorisation of 18 within the prime factorisation of a larger number eg \(54 \times 2^{10} \times 5^6\) and \(54 = 2 \times 3^3\) oe | M1 |
| Answer | Mark | Comments |
|---|---|---|
| \(\sqrt[3]{2^6 \times 11^3}\) or \(\sqrt[3]{64 \times 11^3}\) or \(2^2 \times 11\) or \(4 \times 11\) or \(\sqrt[3]{85\,184}\) | M1 | oe with no fraction in the surd eg \(\sqrt[3]{64 \times 1331}\) oe eg \(2^{(6 \div 3)} \times 11^{(3 \div 3)}\) or \(2^1 \times 2^1 \times 11^1\) |
| 44 | A1 |